SOLUTION: In a given triangle, one side is thrice as long as the shortest side, while the third is 4 inches more than twice the shortest side. Find the perimeter of the triangle in terms of

Algebra ->  Triangles -> SOLUTION: In a given triangle, one side is thrice as long as the shortest side, while the third is 4 inches more than twice the shortest side. Find the perimeter of the triangle in terms of       Log On


   

Question 1176893: In a given triangle, one side is thrice as long as the shortest side, while the third is 4 inches more than twice the shortest side. Find the perimeter of the triangle in terms of the shortest side x. If the perimeter is 54 inches, how long is each of the sides?
Found 2 solutions by ikleyn, math_helper:
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

    x + 3x + (2x+4) = 54


        6x =        = 54 - 4 = 50


         x                   = 50%2F6 = 8 1%2F3  inches.


The sides are  x = 8 1%2F3  inches (shortest);  3x = 25 inches ("one side")  and  (2x+4) = 20 2%2F3  inches  ("the third side").


As always, when you solve such problems, you must check at the end if the triangle inequalities 
are held (to check if a triangle with such sides does really exist).



In this case, the triangle inequalities are valid, so such a triangle does exist.

Solved.



Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


Shortest side: x

Other side:   3x

Third side:   2x+4



    perimeter:   x+(3x)+(2x+4) = 6x+4



If the perimeter is 54in, then the shortest side can be found by: 

    6x+4 = 54

      6x = 50

       x = 50/6 = 25/3   ... shortest side is highlight%28+%2825%2F3%29+in%29 or about 8.333in